To assess prior knowlege, ask students to skip count by 10's. Then ask
a volunteer to name a number they said when they skip-counted. Identify
this as a product. Ask students to name the numbers that they would
multiply together to get that product. Identify these as factors.
Repeat with other numbers in the counting sequence.
10, 20, 30, 40, 50, 60, 70, 80, 90, …
30 = 5 × 6, so 5 and 6 are factors of 30.
To begin the lesson, give each student a copy of the 0—99 Chart and a supply of counters or cubes.
Ask students to cover the numbers that are called as you skip
count by 2’s. Direct students to observe and report the pattern that
results. Note that columns are formed when the numbers are covered in
this counting sequence. Engage students in a discussion about this
pattern and why it occurs.
Have students clear their 0‑99 chart and ask them to cover the
numbers with counters or cubes as you call out the 5’s counting
sequence [5, 10, 15, 20, 25, 30, …]. Ask students to describe the
resulting pattern. Engage students in a discussion about the comparison
between the column pattern created when counting by 2’s and the one
created when counting by 5’s. Encourage students to explain their
Model for students how to count by 3’s and cover the numbers
that are included in this sequence. Discuss how the resulting pattern
compares with the two previous patterns created when counting by 2’s
and 5’s. Invite students to explain how and why the counting pattern
for 3’s is different from the others. Then ask students to clear their
Give each student crayons and tell them that they will now
color the 0‑99 chart that they used in the previous activity. (To
shorten the activity, you may wish to use only the top half of the
chart.) When the students are ready, ask them to skip count by 2's in
unison, coloring each number that they say with a red crayon. It may be
helpful for some students to say 1 softly, 2 loudly, 3 softly, 4 loudly, and so on.
Repeat this same process with counting by 3's and coloring each
number with a yellow crayon. Then have students skip count by 5's,
coloring each number with a blue crayon. (A portion of the completed
chart is shown below.)
Call students' attention to numbers that have been colorded with
more than one crayon. For instance, some numbers on their chart are
orange (colored both red and yellow), and ask students if these numbers
represent a skip-counting pattern. [They will show the pattern of skip
counting by 6; each number is divisible by both 2 and 3.] Repeat with
the numbers that are colored purple (i.e., colored with both red and
blue crayons). [These are products of 10, having both 2 and 5 as
factors.] Ask the students why the number 15 is colored green (i.e.,
colored with both yellow and blue). [It has both 3 and 5 as factors.]
Questions for Students
1. What numbers did you say when you skip count by 2? By 5? By 3? By 10?
[2, 4, 6, 8, etc.; 5, 10, 15, 20, 25, etc.; 3, 6, 9, 12, 15, etc.; 10, 20, 30, 40, 50, etc.]
2. How can we show that 3 × 6 has the same product as 6 × 3?
[3 groups of 6 produces 18; 6 groups of 3 produces 18.]
3. What is similar about skip counting by 5 and adding 5 + 5 + 5? What is
[For both, you get multiples of 5; Counting by 5 can be quicker than adding 5 + 5 + 5.]
4. How does knowing how to skip count by 2 help you skip count by 4?
[Student answers may vary.]
- Which students remembered the commutative property? What experiences are
necessary for those who did not?
- When students were unable to fluently count by 3’s, what strategies would
facilitate their recall of this counting sequence?
- Which students are able to skip count by 2, 3, 5, and 10 rapidly and
correctly? What extension activities would be appropriate for those students?
- What adjustments will I make the next time that I teach this lesson?
- Skip count by twos, threes, fives and tens
- Find products by adding equal sets
- Explore the commutative property of multiplication
Common Core State Standards – Mathematics
Grade 4, Algebraic Thinking
Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule ''Add 3'' and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.